Foundations for Geometry x1 Chapter Test Form B Form A continued Chapter Test · PDF file · 2017-05-119. Name a pair of ... Foundations for Geometry Chapter Test Form A continued

Name ________________________________________ Date ___________________ Class __________________

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Holt McDougal Geometry

Foundations for Geometry Chapter Test Form B

Use the figure for Exercises 1–4.

1. Name a point on line n.

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2. Name a segment on line m.

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3. Name a ray with endpoint C.

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4. Name three collinear points.

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5. F is between E and G, EF = x − 7, and EG = 4x + 3. Find FG.

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6. ,LM QP≅ and LM = 13.5. Find QP.

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7. m�LMP = 57�. Classify �LMP as acute, right, or obtuse.

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8. Z is in the interior of �WXY. m�WXZ = 40�, and m�WXY = 110�. Find m�ZXY.

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9. Name a pair of adjacent angles that do NOT form a linear pair.

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10. �A and �B are complementary. m�A = (5x + 2)�. Find m�B.

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11. �A and �B are supplementary. m�B = 121�. Find m�A.

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12. Find the area of a square with s = 7.6 centimeters.

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13. Find the area of a triangle that has a base of 4 inches and a height of 7.5 inches.

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Name ________________________________________ Date ___________________ Class __________________



Foundations for Geometry Chapter Test Form A continued

Use the figures for Exercises 12–14.

12. Find the perimeter of the square.

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13. Find the area of the triangle.

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14. Find the circumference of the circle. Express your answer in terms of �.

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15. Find the coordinates of the midpoint of GH with endpoints G(−5, 4) and H(−5, 8).

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16. M is the midpoint of ,RS and M has coordinates (2, 6). R has coordinates (−10, 6). Find the coordinates of S.

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17. Use the Distance Formula to find VW.

2 22 1 2 1( ) ( )d x x y y= − + −

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18. Use the Pythagorean Theorem to find the length of the hypotenuse.

a2 + b2 = c2

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19. Identify the transformation as a reflection, a rotation, or a translation.

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20. The coordinates of the endpoints of a segment are A(−2, 3) and B(2, 1). Find the coordinates for the endpoints of the image of AB after the translation (x, y) → (x + 3, y − 2).

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Foundations for Geometry Chapter Test Form C


1. Name the plane containing line m.

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2. Name a segment that has only one point on line n.

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3. Name a pair of rays on plane P that contain B but do not have B as an endpoint.

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4. Name three coplanar points NOT on plane P .

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5. S is the midpoint of ,RT RS = 2x + 4, and RT = 8x. Find ST.

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6. M bisects ,QP and QP = 27.4. Find QM.

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7. m�LMP = 132�. Classify the angle as acute, right, or obtuse.

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8. XZ bisects �WXY, and m�WXZ = 65�. Find m�WXY.

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9. Name a pair of vertical angles.

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10. An angle measures three times the measure of its supplementary angle. Find the measure of both angles.

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11. An angle measures 10� less than the measure of its complementary angle. Find the measure of both angles.

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Name ________________________________________ Date ___________________ Class __________________



Foundations for Geometry Chapter Test Form B continued

14. Find the circumference of a circle with a diameter of 6 feet. Use 3.14 for �.

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15. Find the coordinates of the midpoint of GH with endpoints G(−7, 3) and H(5, 9).

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16. M is the midpoint of ,RS and M has coordinates (−1, 5). R has coordinates (−5, 2). Find the coordinates of S.

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17. Use the Distance Formula to find AB.

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18. Use the Pythagorean Theorem to find VW.

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19. Identify the transformation.

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20. A triangle has vertices at A(−2, 3), B(2, 1), and C(1, 0). After a transformation, the image of the triangle has vertices at A′(−2, −3), B′(2, −5), and C′(1, −6). Identify the transformation.

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Geometric Reasoning Chapter Test Form B

1. Find the next item in the pattern. 1, 2, 3, 5, 8, 13, . . .

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2. Show that the conjecture is false by finding a counterexample. The difference of two odd numbers is a prime number.

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3. Identify the hypothesis and conclusion of the statement “If an angle has a measure less than 90°, then the angle is acute.”

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4. Write True or False. If a number is a prime number, then it is an odd number.

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5. Write the inverse of the conditional statement “If the sum of two whole numbers is even, then both addends are even.”

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6. Given: If a ray bisects an angle, two congruent angles are formed.

YW⎯→

bisects ∠XYZ. Conjecture: ∠XYW ≅ ∠WYZ Determine whether the conjecture is valid by the Law of Detachment.

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7. Given: If a number is a prime number, then it is an odd number. If a number is not divisible by 2, then it is an odd number. Conjecture: If a number is not divisible by 2, then it is a prime number. Determine whether the conjecture is valid by the Law of Syllogism.

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8. A square is a rectangle with four congruent sides. Write the definition as a biconditional.

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9. Solve the equation. Write a justification for each step.

5m − 3 = 22

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Name ________________________________________ Date ___________________ Class __________________



Geometric Reasoning Chapter Test Form A continued

10. Use the Reflexive Property of Congruence to complete the statement “∠A ≅ ________.”

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11. Complete the sentence “A _________ is any statement that you can prove.”

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12. What is the reason for Step 2?

Statements Reasons

1. ∠1 ≅ ∠2 and ∠2 ≅ ∠3.

1. Given

2. m∠1 = m∠2 and m∠2 = m∠3.

2. ?

3. m∠1 = m∠3 3. Trans. Prop. of =

4. ∠1 ≅ ∠3 4. Def. of ≅ �

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13. The box is part of a flowchart proof. Identify the statement.

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14. Write True or False. A paragraph proof is less formal than a two-column proof, so you do not need to include every step.

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Geometric Reasoning Chapter Test Form C

1. Find the next item in the pattern. –1, 0, 3, 8, 15, . . .

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2. Show that the conjecture is false by finding a counterexample. ⏐−x⏐ = x.

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3. Write “A number divisible by 10 is divisible by 5” as a conditional statement in the form “if p, then q.”

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4. Write True or False. A positive whole number that ends in zero can be written as the product of two numbers that do not end in zero.

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5. Write the contrapositive of the conditional statement “If two angles are supplements of the same angle, then the angles have the same measure.”

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6. Given: If two angles are complementary, then the angles are acute. ∠X and ∠Y are both acute. Conjecture: ∠X and ∠Y are complementary. Determine whether the conjecture is valid by the Law of Detachment.

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7. Given: If the area of a circle is numerically equal to the circumference of the circle, then twice the radius is equal to the square of the radius. If twice the radius is equal to the square of the radius, then the diameter is equal to the square of the radius. Draw a conclusion from the given information.

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8. Determine whether the biconditional statement is true. If false, give a counterexample. It is Monday if and only if it is not the weekend.

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9. Solve the equation. Write a justification for each step.

3 = 6x + 1

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10. Use the Transitive Property of Congruence to complete the statement “If AB CD≅ and CD EF≅ , then ________.”

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Name ________________________________________ Date ___________________ Class __________________



Geometric Reasoning Chapter Test Form B continued

10. Use the Symmetric Property of Congruence to complete the statement “If ∠ABC ≅ ∠XYZ, then ∠XYZ ≅ _________.”

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Use the partially completed two-column proof for Exercises 11 and 12. Given: ∠ABC is a right angle, X is in the

interior of ∠ABC, and m∠XBC = 45°.

Prove: BX bisects ∠ABC. Proof:

Statements Reasons

1. ∠ABC is a right angle.

1. Given

2. ? 2. Def. of rt. ∠

3. X is in the interior of ∠ABC.

3. Given

4. m∠ABX + m∠XBC = m∠ABC

4. ∠ Add. Post., Steps 1, 3

5. m∠XBC = 45° 5. Given

6. m∠ABX + 45° = 90° 6. ?

7. m∠ABX = 45° 7. Subtr. Prop. of =

8. ∠ABX ≅ ∠XBC 8. Def. of ≅ �

9. BX bisects ∠ABC. 9. Def. of ∠ bisector

11. Identify the statement that belongs in Step 2.

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12. Identify the justification for Step 6.

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13. Complete the sentence “A flowchart proof uses ________ to show the structure of the proof.”

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14. Given the two-column proof, write a paragraph proof.

Given: ∠1 ≅ ∠2 and ∠2 ≅ ∠3. Prove: ∠1 ≅ ∠3 Proof:

Statements Reasons

1. ∠1 ≅ ∠2 and ∠2 ≅ ∠3.

1. Given

2. m∠1 = m∠2 and m∠2 = m∠3.

2. Def. of ≅ �

3. m∠1 = m∠3 3. Trans. Prop. of =

4. ∠1 ≅ ∠3 4. Def. of ≅ �

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Parallel and Perpendicular Lines Chapter Test Form B

1. Identify a segment perpendicular to .AD

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2. Write True or False. Skew lines can intersect.

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3. How many pairs of corresponding angles are formed by two lines and a transversal?

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4. What type of angle pair are ∠8 and ∠6?

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5. If parallel lines are intersected by a transversal, at most how many different angle measures are there?

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6. Complete the sentence. When parallel lines are cut by a transversal, the angles formed are either ________ or supplementary.

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7. Find the measure of ∠FDE.

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Use the figure for Exercises 8 and 9.

8. Given: ∠8 ≅ ∠2. Identify the postulate or theorem that proves that r || s.

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9. If ∠2 = 4x� and ∠6 = (3x + 25)�, what value of x makes the lines parallel?

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10. Complete the theorem. If two intersecting lines form a linear pair of congruent angles, then the lines are ________.

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11. Name the shortest segment from B to .AC

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Name ________________________________________ Date ___________________ Class __________________



Parallel and Perpendicular Lines Chapter Test Form A continued

12. Write and solve an inequality for x.

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13. The Perpendicular Transversal Theorem states that in a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. Complete the sentence. In a proof, this theorem is used to prove that two lines are ________.

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14. Complete the sentence. The slope of a line is the ratio of the ________ to the run.

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15. Find the slope of JK through J(1, 1) and K(2, 3).

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16. Complete the sentence. If two lines have the same slope and different y-intercepts, then the lines are ________.

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17. Write True or False. The graph of x = 5 is a vertical line.

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18. Write the equation of the line through (3, 4) and (2, 1) in slope-intercept form.

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19. Write the equation of the line through

(4, 6) with slope 34

in point-slope form.

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20. Determine whether the lines are parallel, intersect, or coincide.

y = −3x + 4 y = −3x − 8

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Parallel and Perpendicular Lines Chapter Test Form C

1. Identify a pair of skew segments.

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2. Write True or False. Perpendicular lines cannot be skew lines.

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3. How many total pairs of both alternate exterior and alternate interior angles are formed by a transversal that intersects two coplanar lines at two different points?

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4. Given: ∠8 and ∠6 are corresponding angles. Identify the transversal.

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5. If parallel lines are intersected by a transversal that is not perpendicular to them, how many pairs of nonadjacent supplementary angles are formed?

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6. What one word completes the following sentence? ________ angles formed by a transversal of parallel lines are congruent and all the ________ angles are supplementary to all the obtuse angles.

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7. Find the measure of ∠QRS and state the postulate or theorem that justifies your answer.

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8. If ∠1 ≅ ∠6 and m∠1 ≠ 90�, is r || s?

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9. Which values for x and y make lines r, s, and t parallel?

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10. If two parallel lines and a transversal form angles that are all congruent, describe the relationship between the transversal and each of the parallel lines.

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Name ________________________________________ Date ___________________ Class __________________



Parallel and Perpendicular Lines Chapter Test Form B continued

12. Write and solve an inequality for x.

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13. Complete Step 6 by stating the theorem that proves p || q.

Given: s � p and ∠1 and ∠2 are complementary.

Prove: p || q Proof:

Statements Reasons

1. s � p and ∠1 and ∠2 are complementary.

1. Given

2. m∠1 + m∠2 = 90� 2. Def. of comp. �

3. m∠HJK = m∠1 + m∠2

3. ∠ Add. Post.

4. m∠HJK = 90� 4. Trans. Prop. of =

5. s � q 5. Def. of �

6. p || q 6. ?

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14. Complete the sentence. If the product of the slopes of two lines equals −1, then the lines are _______.

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15. Determine the slope of the line through J(−4, 3) and K(6, 4).

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16. Determine whether the line through (0, 4) and (2, 0) and the line through (−2, 3) and (−4, 2) are parallel, perpendicular, or neither.

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17. Write the equation of the line through (0, 4) and (2, 0) in slope-intercept form.

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18. Write the equation of the line through (4, 4) and (2, 2) in point-slope form.

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19. Write True or False. y = −3x + 4 and y = 3x + 4 are parallel.

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20. Determine whether the lines 3x + 2y = 6 and 4y = −6x −12 are parallel, intersect, or coincide.

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Triangle Congruence Chapter Test Form B

1. Identify and describe the transformation: M: (x, y) → (x � 4, y – 6)

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2. Are triangles A(1, 7), B(2, 8), C(3, 7) and D(2.5, 17.5), E(5, 20), F(7.5, 17.5) congruent? Describe the transformation that supports your answer.

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3. Classify �ABD by its angle measures.

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4. Classify �ABC by its side lengths.

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5. The measure of the smallest angle of a right triangle is 27°. What is the measure of the second to smallest angle?

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6. Find the measure of ∠RST.

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7. �JKL ≅ �MNP, KL = 21x − 2, NP = 20x, LJ = 15x, PM = 13x + 4. Find LJ.

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8. Given: �TUV ≅ �TWV. Find m∠U and UV.

________________________________________ 9. Given: ∠5 ≅ ∠6, ∠3 ≅ ∠4, DE FE≅ ,

≅ ≅, .FG DG GE GE Provide an additional statement and a reason for that statement to prove �DEG ≅ �FEG by the definition of congruent triangles.

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10. If AB = 3x − 7 and DC = 2x + 1, what value of x proves �AEB ≅ �CED by the SSS Postulate?

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11. What postulate or theorem proves �AED ≅ �CEB?

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12. If ∠DAB ≅ ∠ADC, what additional congruence statement do you need to prove �DAB ≅ �ADC by the ASA Postulate?

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13. If ∠ABC and ∠CDA are right angles and AB CD≅ , what postulate or theorem proves �ABC ≅ �CDA?

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Name ________________________________________ Date ___________________ Class __________________



Triangle Congruence Chapter Test Form A continued

14. Write True or False. To give a coordinate proof about a right triangle, it is a good idea to position the vertex of the right angle at (0, 0) so that the legs are on the positive sides of the axes.

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15. Write True or False. The Midpoint Formula is used in the coordinate proof to prove the statement

EF = 12

RS .

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16. Find the value of x.

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17. What postulate or theorem proves ∠K ≅ ∠M?

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18. Write True or False. Given: �ABC and �DEF. To use CPCTC to prove ∠A ≅ ∠D, you must first prove �ABC ≅ �DEF.

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Triangle Congruence Chapter Test Form C

1. Identify and describe the transformation: M: (x, y) → (-x, y)

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2. Prove that triangles F(4, 6), G(5, 7), H(7, 4) and J(1, -4), K(2, -5), L(4, -2) are congruent.

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3. Classify �ABC by angle measures.

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4. Classify �ABD by side lengths.

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5. What is m∠T ?

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6. What is the value of y?

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7. Given �QRS ≅ �STQ, ∠R = 4x2 − 4, and ∠T = 3x2 − 3x. What is m∠R?

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8. Given �QRS ≅ �STQ, RS = 3x − 3, TQ = 2x + 2, and QR = x2 − 2. What is the length of side ?ST

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9. Prove �TUV ≅ �TWV by using the definition of congruent triangles.


10. If AD BC≅ , write a statement about point E that would allow you to prove �AED ≅ �CEB by the SSS Postulate.

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11. Suppose AE CE≅ and DEBE ≅ . What postulate or theorem will allow you to prove �BEA ≅ �DEC?

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12. Write True or False. If ∠ABC and ∠DCB are right angles and ,AD BC you can prove �ABC ≅ �DCB.

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13. ∠DAB and ∠BCD are right angles. Write a single congruence statement about two segments that would allow you to conclude that �DAB ≅ �BCD. What theorem or postulate would justify the conclusion?

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Name ________________________________________ Date ___________________ Class __________________



Triangle Congruence Chapter Test Form B continued

Use the Given information for Exercises 14 and 15. Given: An isosceles triangle ABC with

AB BC≅ and a perpendicular bisector BD from B to .AC

14. Position the figure in the coordinate plane and assign coordinates to each point so proving that the area of �ABD is equal to the area of �CBD using a coordinate proof would be easier to complete.

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15. Write a coordinate proof to prove that the area of �ABD is equal to the area of �CBD.

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Use the figure and the partially completed two-column proof for Exercises 17 and 18. Given: ∠BAC ≅ ∠BCA

Prove: AD CE≅

Proof:

17. What is the justification for Step 2?

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18. What is the justification for Step 6?

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Statements Reasons

1. ∠BAC ≅ ∠BCA 1. Given

2. BA BC≅ 2. ?

3. ∠D and ∠E are right s∠ .

3. Given (diagram)

4. DB EB≅ 4. Given (diagram)

5. �DBA ≅ �EBC 5. HL Congruence Thm.

6. AD CE≅ 6. ?

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Properties and Attributes of Triangles Chapter Test Form B

1. Find AB.

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2. The line y = 2x + 3 is the perpendicular bisector of MN and intersects MN at (−6, −9). Find an equation of MN in point-slope form.

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3. Find m∠DEY.

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4. , ,ZX ZY and ZW are the perpendicular bisectors of �TUV. Find XT, VU, and ZV.

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5. GX and XJ are angle bisectors of �GHJ. Find m∠HJX and the distance from X to GH .

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6. If MX = 21.6, find LZ and MW.

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7. Find the coordinates of the orthocenter of the triangle.

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8. Find the perimeter of �ABC.

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Name ________________________________________ Date ___________________ Class __________________



Properties and Attributes of Triangles Chapter Test Form A continued

10. Write True or False. In an indirect proof, you always assume that the opposite (or negation) of the conclusion is true.

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11. Write True or False. The measures 10, 12, and 16 can be the side lengths of a triangle.

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Use the figures for Exercises 12 and 13.

12. Write the sides of �FED in order from smallest to largest.

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13. Compare FD and GJ.

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15. Write True or False. A right triangle has sides that measure 5, 12, and 13. The side lengths form a Pythagorean triple.

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16. The measures of the side lengths of a triangle are 3, 4, and 5. Classify the triangle as acute, right, or obtuse.

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18. Find the values of x and y.

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Properties and Attributes of Triangles Chapter Test Form C

1. In �ABC, B is on the perpendicular bisector of AC , m∠A = (6x + 14)�, and m∠ABC = (10x − 2)�. Find m∠C.

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2. Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints (2, 4) and (6, 2).

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3. Find m∠DEF.

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4. Find the center of the circle circumscribed about the triangle with vertices (0, 0), (8, 0), and (6, 4).

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5. TG and GV are angle bisectors of �TUV. Find m∠VGT and the distance from G to .UV

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6. Find the coordinates of the centroid of the triangle with vertices at (−4, −2), (1, 2), and (6, 3).

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7. Find the coordinates of the orthocenter of �TUV with T(0, 0), U(4, 4), and V(1, 7).

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9. What is m∠TAC?

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10. Use indirect reasoning to explain why an obtuse triangle cannot have a right angle.

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Name ________________________________________ Date ___________________ Class __________________



Properties and Attributes of Triangles Chapter Test Form B continued

9. Find m∠QSP.

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10. In an indirect proof to prove that m∠P > m∠Q, what is an assumption you must make about m∠P and m∠Q?

_________________________________________

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11. Write True or False. A triangle can have sides of lengths 7.5, 4.5, and 12.5.

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Use the figures for Exercises 12 and 13.

12. Order the sides of �KLM from smallest to largest.

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13. Find the range of values for x.

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14. The hypotenuse and one leg of a right triangle measure 26 and 10, respectively. Find the measure of the third side.

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15. The legs of a right triangle measure 3 and 5, respectively. Determine whether the side lengths form a Pythagorean triple and, if not, why not.

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16. Classify the triangle with side lengths of 16, 7, and 12.

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17. One leg of a 45�-45�-90� triangle is 3 2 . Find the length of the hypotenuse.

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18. The longer leg of a 30�-60�-90� triangle is 5 3 . Find the length of the hypotenuse.

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Polygons and Quadrilaterals Chapter Test Form B

1. Name the polygon by its number of sides and tell whether it is regular or irregular.

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2. Find the measures of each interior angle of a regular octagon.

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3. Find the value of a.

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4. Write a biconditional statement to define the term parallelogram.

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5. ABCD is a parallelogram. Find AB and BX.

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6. EFGH is a parallelogram. Find m∠E.

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7. Write True or False. The quadrilateral must be a parallelogram.

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8. Show that JKLM is a parallelogram for x = 7 and y = 14.

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9. Complete the sentence. A ________ is a parallelogram that has the properties of both a ________ and a ________.

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10. ABCD is a rectangle with diagonals BD and AC that intersect at X. BD = 12x − 6 inches and AX = 4x + 5 inches. Find DX.

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Name ________________________________________ Date ___________________ Class __________________



Polygons and Quadrilaterals Chapter Test Form A continued

11. RSTU is a rhombus. m∠SRU = 112. Find m∠TRU.

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12. Write True or False. If ||EF HG and ||EH FG , then EFGH is a rectangle.

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13. Given: UVWX is a parallelogram and ≅ .UV XU

Conclusion: UVWX is a rhombus. Determine whether the conclusion is valid.

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14. In kite JKLM, m∠JMN = 25°. Find m∠NJM.

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15. In trapezoid ABCD, find m∠A.

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16. Find the length of the midsegment of trapezoid PQRS.

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Polygons and Quadrilaterals Chapter Test Form C

1. Identify the figure as specifically as possible.

_________________________________________

2. An interior angle of a regular convex polygon measures 144°. How many sides does the polygon have?

_________________________________________

3. The exterior angles of a convex pentagon measure (18x + 12)°, 16x°, (8x+ 6)°, (10x − 12)°, and (5x + 12)°. Determine the measure of the largest interior angle.

_________________________________________

4. Three vertices of parallelogram PQRS are P(−1, 3), Q(4, 1), and R(1, −2). Find the coordinates of vertex S.

_________________________________________

5. Given ,ABCD determine the value of y.

_________________________________________

6. In ,EFGH the diagonals intersect at Y. If EY = x2 and GY = 2x + 3, determine the length of EG .

_________________________________________

7. Prove that JKLM is a parallelogram.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

8. Use the definition of parallelogram to show that the quadrilateral with vertices A(−4, 4), B(−2, 0), C(6, 4), and D(4, 8) is a parallelogram.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

9. Give the best name for the quadrilateral with vertices (−2, 1), (−3, −2), (4, −1), and (3, −4).

________________________________________

Name ________________________________________ Date ___________________ Class __________________



Polygons and Quadrilaterals Chapter Test Form B continued

11. RSTQ is a rhombus. Find m∠PST.

_________________________________________

12. Given: WXYZ is a parallelogram. WY and XZ bisect each other and

⊥ .WY XZ Conclusion: WXYZ is a rectangle.

Determine whether the conclusion is valid. If not, tell why not.

_________________________________________

_________________________________________

_________________________________________

_________________________________________

_________________________________________

_________________________________________

_________________________________________

13. Tell whether the parallelogram is a rectangle, rhombus, or square.

_________________________________________

_________________________________________

14. In kite JKLM, m∠LMN = 25°, and m∠LKN = 43°. Find m∠MLK.

________________________________________

15. In trapezoid ABCD, find m∠A.

________________________________________

16. XY is the midsegment of trapezoid ABCD. Find AB.

________________________________________

Chapter

x

116

Chapter

6

116


Name ________________________________________ Date ___________________ Class __________________



Similarity Chapter Test Form B

1. Determine whether �ABC and �DEF are similar. If so, write the similarity ratio and a similarity statement.

_________________________________________

2. Jamestown, North Dakota, claims to have the world�s largest bison (American buffalo) statue. The statue is 26 feet high, 46 feet long, and 14 feet wide. The statue is similar to an actual bison that is 6 feet tall. About how long is the actual bison to the nearest foot?

_________________________________________

3. The scale drawing of a triangular swimming pool has the dimensions shown. The longest side of the actual swimming pool is 8 m. What is the length of the actual swimming pool?

_________________________________________

4. Give an example of a transformation that is NOT a similarity transformation.

_________________________________________

5. Describe the dilation

D: (x, y) → ⎛ ⎞⎜ ⎟⎝ ⎠

4 4, .5 5

x y

________________________________________

________________________________________

6. Tell how polygon A(0, 0), B(5, 4), C(3, 2), D(–1, –1) was mapped to polygon E(2, 2.5), F(4.5, 4.5), G(3.5, 3.5), H(1.5, 2).

________________________________________

________________________________________

7. Explain why the triangles are similar and write a similarity statement.

________________________________________

________________________________________

________________________________________

________________________________________

8. Find SP.

________________________________________

Name ________________________________________ Date ___________________ Class __________________



Similarity Chapter Test Form A continued

10. Find RQ.

_________________________________________

11. Mentone, Indiana, claims to have the world's largest egg sculpture. A 6-foot-tall person standing next to the egg sculpture casts a shadow that is 2 feet long. If the egg casts a shadow that is 4 feet long, how tall is the sculpture?

_________________________________________

12. A drawing of a garden uses a scale of 1 in : 3 ft. Find the length of the garden if the length on the drawing is 13 inches.

_________________________________________

13. Given that �UOV is a dilation image of �SOT, find the coordinates of V and the scale factor.

________________________________________

14. Given: A(0, 0), B(0, 3), C(4, 0), D(0, 6), and E(8, 0) Prove: �ABC ∼ �ADE

________________________________________

________________________________________

________________________________________

________________________________________

Chapter

x

135

Chapter

7

135


Name ________________________________________ Date ___________________ Class __________________



Similarity Chapter Test Form C

1. AB is a midsegment of �ECD. Point A is on EC , and point B is on .CD Determine whether the two triangles formed are similar. If so, write the similarity ratio and a similarity statement.

_________________________________________

2. The scale for a blueprint is 1 : 50. What is the length on the blueprint for a bathroom wall that is 150 inches long?

_________________________________________

3. A star-shaped garden has the dimensions shown. A scale drawing of the garden has the dimension shown. Find x to the nearest hundredth of an inch.

_________________________________________

4. Give an example of a transformation that is NOT a similarity transformation.

_________________________________________

5. Describe the dilation

D: (x, y) → ⎛ ⎞⎜ ⎟⎝ ⎠

7 7, .8 8

x y

_________________________________________

_________________________________________

6. Tell how polygon E(5, 0), F(9, 4), G(7, 2), H(0, –1) was mapped to polygon J(12, 6), K(18, 12), L(15, 9), M(4.5, 4.5).

________________________________________

________________________________________

7. Given: SR = 2RU and ST = 2TV. Prove: �USV ∼ �RST

8. Find DE.

________________________________________

9. Find AX.

________________________________________

Name ________________________________________ Date ___________________ Class __________________



Similarity Chapter Test Form B continued

9. What is BC?

_________________________________________

10. Find PR.

_________________________________________

11. One afternoon, a student who is 5 feet 4 inches tall measured shadows to find the height of a telephone pole. The student’s shadow was 5 feet long. At the same time, the shadow of the telephone pole was 18 feet 9 inches long. How tall is the telephone pole?

_________________________________________

12. A blueprint for an art gallery uses a scale of 1 in : 4 ft. One of the rooms in the

gallery measures 3 12

inches long on the

blueprint. How long is the actual room?

_________________________________________

13. Given that �UOV is a dilation image of �SOT, find the coordinates of U and the scale factor.

________________________________________

14. Given: A(2, 1), B(6, 3), C(8, 1), D(4, 2), and E(5, 1) Prove: �ABC ∼ �ADE

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Chapter

x

136

Chapter

7

136


Name ________________________________________ Date ___________________ Class __________________



Right Triangles and Trigonometry Chapter Test Form B

1. Find AB. If necessary, give the answer in simplest radical form.

_________________________________________

2. Find the area of WYZ. If necessary, give the answer in simplest radical form.

_________________________________________

3. Find sinB as a decimal rounded to the nearest hundredth.

_________________________________________

4. Use a special right triangle to write cos45� as a fraction.

_________________________________________

5. Find SR. Round to the nearest whole number.

________________________________________

6. From a point on the ground 12 feet in front of the building, the angle of elevation to the top of the building is 76�. How tall is the building? Round the answer to the nearest foot.

________________________________________

7. To the nearest degree, what is m∠A?

________________________________________

8. Near Pittsburgh, a cable car transports people from the Monongahela River valley to the community on top of the overlooking bluff. The Monongahela Incline has a grade of 78%. Find the measure of the angle the cable car track makes with the valley floor. If necessary, round to the nearest degree.

________________________________________

Name ________________________________________ Date ___________________ Class __________________



Right Triangles and Trigonometry Chapter Test Form A continued

9. Classify ∠3 as an angle of elevation or angle of depression.

_________________________________________

10. When the angle of elevation of the sun is 63�, a tree casts a shadow that is 27 feet long. To the nearest foot, how tall is the tree?

_________________________________________

11. Tell whether you would use the Law of Sines or the Law of Cosines to find DF.

_________________________________________

12. Find BC to the nearest whole number.

________________________________________

Use the graph for Exercises 13 and 14.

13. Find the magnitude of ⟨3, 4⟩.

________________________________________

14. Find the direction of ⟨3, 4⟩ to the nearest degree.

________________________________________

15. A classroom has a window near the ceiling, and a long pole is used to close the window. The force applied to the window is described by the vector ⟨6, 8⟩. Find the magnitude and direction of the force.

________________________________________

Chapter

x

155

Chapter

8

155


Name ________________________________________ Date ___________________ Class __________________



Right Triangles and Trigonometry Chapter Test Form C

1. Find x, y, and z.

_________________________________________

2. A photographer positions a camera on a tripod to take a picture of a grain silo. The lens of the camera is 4 feet 6 inches from the ground. To get the full height of the silo, the camera had to be positioned 18 feet from the base of the silo. How tall is the grain silo?

_________________________________________

3. Determine the value of cosB to the nearest hundredth.

_________________________________________

4. Complete the chart.

30� 45� 60�

sin

cos

tan

5. Find the perimeter and area of the triangle. Round to the nearest tenth.

________________________________________

6. Find YZ. Round to the nearest unit.

________________________________________

7. Find m∠D to the nearest degree.

________________________________________

8. The length of a slide at a water park is 50 feet from the top of the slide to ground level. The top of the slide is 20 feet above the ground. What is the approximate measure of the angle formed by the top of the slide and the vertical support to the ground? Round to the nearest degree.

________________________________________

Name ________________________________________ Date ___________________ Class __________________



Right Triangles and Trigonometry Chapter Test Form B continued

9. The angle of elevation from a person lying on the ground to a hot-air balloon is 37�. The balloon is at an altitude of 1500 feet. To the nearest foot, find the horizontal distance from the person to a point on the ground directly below the balloon.

_________________________________________

10. The angle of depression from a plane to the airport is 34�. The pilot reports that the plane’s altitude is 3200 feet. Find the horizontal distance between the plane and the airport to the nearest foot.

_________________________________________

11. A triangle has angle measures of 40�, 59�, and 81�. The side opposite the 40� angle is 11 centimeters long. Find the length of the side opposite the 81� angle to the nearest centimeter.

_________________________________________

12. Find JL. Round the answer to the nearest tenth.

________________________________________

13. Find the magnitude of PQ with initial point P(−4, −7) and terminal point Q(1, −3).

________________________________________

14. The current of a river is given by the vector ⟨4, 2⟩. Find the direction of the vector to the nearest degree.

________________________________________

15. A small plane flies at a constant speed of 300 miles per hour on a bearing of N 55� E. There is a 30 mile per hour wind blowing due east. Find the plane’s actual speed and direction. Round the speed to the nearest tenth.

________________________________________

Chapter

x

156

Chapter

8

156


Name ________________________________________ Date ___________________ Class __________________



Transformational Geometry Chapter Test Form B

1. Draw the reflection of the figure across the line.

2. Identify the image of the point A(−6, −9) when A is reflected across the line y = x.

_________________________________________

3. �ABC has vertices A(−4, −2), B(−1, 4), and C(0, −1). Draw �ABC and its image �A′B′C′ for translation along the vector ⟨2, −1⟩.

4. After a translation, the image of P(−3, 5) is P′(−4, 3). Identify the image of the point (1, −6) after this same translation.

_________________________________________

5. Draw the rotation of the triangle about the origin by 90�.

6. If the image of point J under a 180� rotation about the origin is (7, −3), what are the coordinates of point J?

________________________________________

7. �RST is rotated 90� about the origin. Then its image is reflected across the x-axis. Draw �R″S″T″ under this composition of transformations.

8. Determine the angle of rotation if an image is the result of a composition of two reflections across perpendicular lines.

________________________________________

Name ________________________________________ Date ___________________ Class __________________



Transformational Geometry Chapter Test Form A continued

9. Identify a single transformation that is equivalent to reflecting the figure across line n and then reflecting the image across line m.

_________________________________________

10. Write True or False. The figure has line symmetry. If true, tell how many lines of symmetry.

_________________________________________

11. Write True or False. The figure has rotational symmetry.

_________________________________________

12. Write True or False. The pattern is a tessellation.

_________________________________________

13. Identify a pair of regular polygons that can be used to make a semiregular tessellation.

________________________________________

14. Write True or False. The transformation is a dilation.

________________________________________

15. Identify the coordinates of the image of vertex M under a dilation centered at the

origin with a scale factor of 12

.

________________________________________

Chapter

x

175

Chapter

9

175


Name ________________________________________ Date ___________________ Class __________________



Transformational Geometry Chapter Test Form C

1. Determine the coordinates of the image when the point P(−6, −2) is reflected across the line x = −4.

_________________________________________

2. Two cabins are on the same side of a river. Two trails are planned to connect the campsites to a planned boat dock on the river. On a grid, cabin A would be at (4, 2), cabin B would be at (−2, 4), and the river would be located along the x-axis. Where should the dock be located to make the combined length of the trails as short as possible?

_________________________________________

3. The point R(2, −3) is translated along a vector that is parallel to the line y = 2x + 1. The translation vector has a magnitude of 2 5 . What are the coordinates of a possible image of point R?

_________________________________________

4. Given the function y = x2, write a function that reflects the graph across the x-axis.

_________________________________________

5. A revolving restaurant takes 36 minutes to complete one rotation. If a table that is 32 feet from the center of the restaurant is represented by the coordinates (32, 0), determine the coordinates of the table after 6 minutes. Round coordinates to the nearest tenth if needed.

_________________________________________

6. Use mapping notation to represent a 90� clockwise rotation about the origin of the point (x, y).

________________________________________

7. The point (2, −3) is reflected across the line y = 1 and then rotated 90� about the origin. Determine the final coordinates of the image after the composition of transformations.

________________________________________

8. A figure above the line y = −1 is reflected across the line y = −1 and then reflected across the line y = −5. Determine the slope and magnitude of the equivalent translation vector.

________________________________________

9. Suppose the triangle shown is reflected across line n and then across line m. Describe a single transformation that is equivalent to this composition of transformations.

________________________________________

Name ________________________________________ Date ___________________ Class __________________



Transformational Geometry Chapter Test Form B continued

9. �KLM with vertices K(2, 1), L(4, 3), and M(4, 1) is reflected across the x-axis, and then its image is reflected across the line y = x. Identify a single transformation that moves the triangle from its starting position to its final position.

_________________________________________

10. Tell whether the figure has line symmetry. If so, tell how many lines of symmetry.

_________________________________________

11. Tell whether the figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of symmetry.

_________________________________________

12. Tell whether the regular polygon can be used to form a tessellation. If not, tell why not. If so, draw the tessellation.

_________________________________________

_________________________________________

_________________________________________

13. Tell whether the regular polygons can be used to form a tessellation. If so, tell how many of each polygon must meet at each vertex.

________________________________________

14. Write True or False. The large triangle is a dilation image of the small triangle.

________________________________________

15. Draw the image of the figure with vertices A(−1, 1), B(1, 2), and C(3, −2) under a dilation centered at the origin with a scale factor −2.

Chapter

x

176

Chapter

9

176


Name ________________________________________ Date ___________________ Class __________________



Extending Perimeter, Circumference, and Area Chapter Test Form B

1. Find the area of the triangle.

_________________________________________

2. Find the area of the parallelogram.

_________________________________________

3. Find the area of the rhombus.

_________________________________________

4. The area of the trapezoid is 34.5 square feet. Find the base.

_________________________________________

5. Find the area of the kite.

_________________________________________

6. The perimeter of a rhombus is 40 inches. One diagonal is 12 inches. Find the area of the rhombus.

________________________________________

7. Find the radius of P in which C = 36π cm.

________________________________________

8. Given that the circle is inscribed in the square, find the area of the circle to the nearest hundredth.

________________________________________

9. Find the area of the regular polygon to the nearest tenth.

________________________________________

10. The figure is a semicircle with a radius of 8 inches. Find the area of the shaded part of the figure to the nearest hundredth.

________________________________________

Name ________________________________________ Date ___________________ Class __________________



Extending Perimeter, Circumference, and Area Chapter Test Form A continued

11. Estimate the area of the figure. The grid has squares with side lengths of 1 inch.

_________________________________________

Use the grids for Exercises 12–14. 12. Find the perimeter of the polygon with

vertices A(−2, 1), B(−2, 3), C(1, 3), and D(1, 1).

_________________________________________

13. Find the area of the polygon with vertices A(−2, −1), B(−2, 3), C(1, 3), and D(1, 1).

_________________________________________

14. Find the area of the polygon with vertices D(−1, 3), E(2, 3), and F(2, −5).

________________________________________

15. If the radius of a circle is multiplied by 2, describe the effect on the circumference.

________________________________________

16. A gardener wants to double the area of a rectangular flower bed. Describe how the dimensions should be changed.

________________________________________

17. Find the probability that a dart that hits the large rectangular target at a random point will hit inside the square.

________________________________________

18. A stoplight is green for 30 seconds, yellow for 5 seconds, and red for 25 seconds. What is the probability that the light will be green when you arrive?

________________________________________

Chapter

x

195

Chapter

10

195


Name ________________________________________ Date ___________________ Class __________________



Extending Perimeter, Circumference, and Area Chapter Test Form C

1. Express the area of an equilateral triangle in terms of the length s of a side.

_________________________________________

2. Find the area of the parallelogram.

_________________________________________

3. The longer diagonal of a rhombus is equal to 3 times one of its sides. The length of a side is 6 inches. Determine the area of the rhombus. Leave your answer in simplest radical form.

_________________________________________

4. The midsegment of the trapezoid has a length of 11.5 cm. Find the area of the trapezoid.

_________________________________________

5. Find the area of the kite.

_________________________________________

6. The area of an equilateral triangle is equal to the area of a trapezoid. The trapezoid has bases with lengths 4 centimeters and 14 centimeters and an altitude of 4 3 centimeters. Determine the perimeter of the triangle.

________________________________________

7. A circle is circumscribed about a square. The square has side lengths of 8 inches. Find the circumference of the circle in terms of π. Leave your answer in simplest radical form.

________________________________________

8. A regular hexagon is circumscribed about a circle. The circle has a radius of 9 feet. Find the area of the hexagon to the nearest tenth.

________________________________________

9. Find the area of the square.

________________________________________

Name ________________________________________ Date ___________________ Class __________________



Extending Perimeter, Circumference, and Area Chapter Test Form B continued

11. Estimate the area of the figure. The grid has squares with side lengths of 1 yard.

_________________________________________

_________________________________________

12. Find the perimeter of the polygon with vertices A(−5, 2), B(1, 5), C(3, 1), and D(−3, −2). If necessary, leave your answer in simplest radical form.

_________________________________________

13. Find the area of the polygon with vertices D(−1, 2), E(2, 2), F(2, −1), and G(−3, −1).

_________________________________________

14. Find the area of the circle centered at the origin that passes through the point (−3, 5). Round your answer to the nearest tenth of a square unit.

_________________________________________

15. The diameter of a circle is increased by a factor of 3. Describe the effect on the area of the circle.

________________________________________

16. A square sandbox has an area of 8 square feet. If you want to double the area, what size should you make the sides of the new sandbox?

________________________________________

17. Find the probability that a point chosen randomly inside the 60-m-by-30-m rectangle will be inside either the small rectangle or the triangle.

________________________________________

18. A stoplight is green for 28 seconds, yellow for 5 seconds, and red for 27 seconds. What is the probability that the light will NOT be green when you arrive?

________________________________________

Chapter

x

196

Chapter

10

196


Name ________________________________________ Date ___________________ Class __________________



Spatial Reasoning Chapter Test Form C

1. Describe the faces and base(s) of a pentagonal prism.

_________________________________________

2. Describe the cross section formed by the intersection of a triangular pyramid and a plane parallel to the base of the pyramid.

_________________________________________

3. Three inches around both ends of the box will be cut and folded to form the top and bottom. Determine the volume of the box. If necessary, round to the nearest tenth.

_________________________________________

4. To the nearest cubic centimeter, determine the volume of packing peanuts needed to fill the box if the radius of the enclosed cylinder is 4 centimeters and the cylinder is centered in the box.

_________________________________________

5. A square pyramid has a slant height of 17 centimeters and a lateral area of 544 square centimeters. Determine the volume of the pyramid.

________________________________________

6. There is a cone-shaped plug in the bottom of a cone. If the height of the plug is 5 inches and the height of the cone is 16 inches, determine the volume of the cone. If necessary, round to the nearest tenth.

________________________________________

7. Determine the diameter of a sphere with a volume of 972π in3.

________________________________________

8. Find the surface area in terms of π of a sphere with a volume of 288π cm3.

________________________________________

Name ________________________________________ Date ___________________ Class __________________



Spatial Reasoning Chapter Test Form B

1. How would you classify a three-dimensional figure that has a circular base and a vertex?

_________________________________________

2. Describe the three-dimensional figure that can be made from the net.

_________________________________________

3. Find the volume of the regular hexagonal prism. If necessary, round to the nearest tenth.

_________________________________________

4. Find the volume of a cylinder with a base area of 49π in2 and a height equal to twice the radius. If necessary, round to the nearest tenth.

_________________________________________

5. Find the volume of a rectangular pyramid with length 5 meters, width 3.4 meters, and height 8 meters. Round to the nearest tenth.

_________________________________________

6. Find the volume of the cone. Round to the nearest tenth.

________________________________________

7. Determine the volume of a sphere with a great circle that has an area of 9π cm2. Give the answer in terms of π.

________________________________________

8. Determine the surface area of a sphere if the diameter is 3 feet. Round to the nearest tenth.

________________________________________

Chapter

x

210

Chapter

11

210


Name Date Class



Circles Chapter Test Form B

1. Complete the sentence. A secant is a ________ in the plane of a circle that intersects the circle at exactly ________ points.

2. Mount McKinley in Alaska is North America’s highest mountain. The mountain is 20,320 feet high. To the nearest mile, find the distance from the summit to the horizon at sea level.

_________________________________________

3. Find m .CDE

_________________________________________

4. Find BD.

_________________________________________

5. Find the area of sector DEF. Give your answer in terms of π and rounded to the nearest hundredth.

_________________________________________

6. Find the length of .JK Give your answer in terms of π and rounded to the nearest hundredth.

________________________________________

7. Find m∠LPO.

________________________________________

8. Find m∠RSP.

________________________________________

9. If m∠JKM = 58.5�, find m∠NKL.

________________________________________

Name Date Class



Circles Chapter Test Form B continued

10. Find m∠LKA.

_________________________________________


_________________________________________

12. If JL = 12, find KL.

_________________________________________

13. Find the length of .BD

_________________________________________

14. An arrangement of stones that formed an arc of a circle was discovered. If the chord is 12 meters, find the diameter of the completed circle.

________________________________________

15. Write the equation of B with center B(−2, 3) that passes through (1, 2).

________________________________________

16. Graph (x + 1)2 + (y − 2)2 = 16.

17. A new firehouse is being built equidistant from three other fire stations. Positioned on a grid, the current fire stations would be located at (2, 2), (3, −5), and (−5, −5). Find the coordinates of the new firehouse.

________________________________________

Chapter

x

228

Chapter

12

228


Name Date Class



Circles Chapter Test Form B

1. Complete the sentence. A secant is a ________ in the plane of a circle that intersects the circle at exactly ________ points.

2. Mount McKinley in Alaska is North America’s highest mountain. The mountain is 20,320 feet high. To the nearest mile, find the distance from the summit to the horizon at sea level.

_________________________________________

3. Find m .CDE

_________________________________________

4. Find BD.

_________________________________________

5. Find the area of sector DEF. Give your answer in terms of π and rounded to the nearest hundredth.

_________________________________________

6. Find the length of .JK Give your answer in terms of π and rounded to the nearest hundredth.

________________________________________

7. Find m∠LPO.

________________________________________

8. Find m∠RSP.

________________________________________

9. If m∠JKM = 58.5�, find m∠NKL.

________________________________________

Name Date Class



Circles Chapter Test Form B continued

10. Find m∠LKA.

_________________________________________


_________________________________________

12. If JL = 12, find KL.

_________________________________________

13. Find the length of .BD

_________________________________________

14. An arrangement of stones that formed an arc of a circle was discovered. If the chord is 12 meters, find the diameter of the completed circle.

________________________________________

15. Write the equation of B with center B(−2, 3) that passes through (1, 2).

________________________________________

16. Graph (x + 1)2 + (y − 2)2 = 16.

17. A new firehouse is being built equidistant from three other fire stations. Positioned on a grid, the current fire stations would be located at (2, 2), (3, −5), and (−5, −5). Find the coordinates of the new firehouse.

________________________________________

Chapter

x

229

Chapter

12

229


Name ________________________________________ Date ___________________ Class __________________



Probability Chapter Test Form B

1. A movie theater has posters for 7 new movies. How many ways can the theater arrange 5 of the posters on a wall?

_________________________________________ 2. A customer at a bookstore is interested

in 10 books on sale. How many ways can she choose 3 books to buy?

_________________________________________ 3. A man has 4 pairs of dress pants, 4

dress shirts, and 10 ties. How many different ways can he dress for a job interview?

_________________________________________

4. In a new neighborhood, houses are constructed of brick, wood, or cement.

According to the graph above, what is the probability that a house chosen at random is made of brick?

_________________________________________

5. Two number cubes are rolled at the same time. What is the probability that the two cubes show different numbers?

_________________________________________

6. What is the probability that a point chosen inside the rectangle is in the shaded region?

________________________________________

7. A coin and a number cube are tossed at the same time. What is the probability of tossing a tails and rolling a 4 or 5 at the same time?

________________________________________

8. The table shows the results of a consumer survey asking men and women where they prefer to shop.

Shopping By Gender

Male Female

Store A 12 6

Store B 4 14

What is the probability that a person chosen from this group is a male who prefers Store A?

________________________________________

9. Use the two-way table from Question 8. What is the approximate probability that a person prefers store A?

________________________________________

Chapter

13

248

CS10_G_MEAR710334_C13FRT.indd 248CS10_G_MEAR710334_C13FRT.indd 248 5/19/11 5:26:15 PM5/19/11 5:26:15 PM

Name ________________________________________ Date ___________________ Class __________________



Probability Chapter Test Form B continued

10. A biologist has collected data from 320 tidal pools. 125 of the pools contained shrimp and 183 contained algae. There were 147 tidal pools that contained only algae. What is the probability that a tidal pool contains shrimp or algae?

_________________________________________ 11. There are 6 children in the Martinez

family. What is the probability that at least 2 of them were born in the same month?

________________________________ 12. Men and Women at an eyeglass store

were polled to see if they prefer round or square frames. The results of the poll are shown in the two-way table.

Round Square Men 7 1

Women 2 5 How many people were polled?

________________________________ 13. Use the two-way table from Question 12.

How many people prefer square frames?

_________________________________________

14. Use the two-way table from Question 12. Did more people prefer round or square frames?

_________________________________________

15. Of 5 doctors in a small clinic, 4 work the weekends and 2 wear glasses. Which is the probability that one of the doctors works on the weekend or wears glasses?

________________________________________

16. What is the probability a 1-6 number cube lands between 1 and 6?

________________________________________

17. What is the probability that a card drawn from a standard deck is a club and has a letter on it?

________________________________________

Works on Weekend

Wears Glasses

Chapter

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Foundations for Geometry x1 Chapter Test Form B Form A continued Chapter Test · PDF file · 2017-05-119. Name a pair of ... Foundations for Geometry Chapter Test Form A continued